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The torsion tube can apply to the torso but also to the limbs and to the limbs and torso considered in a continuum.

The double pendulum can be considered as the legs from hips to ground plus the torso from hips to head. Each limb may also be separately a double pendulum, or all of them together form a chain of dependent pendula.

At first glance, these models would seem very different, a torsion tube quite static, the double pendulum quite dynamic, but the structure and dynamic of these models are, in fact, closely related.

The effect of the torque creates shear on the radial and longitudinal axis of the tube. The diagonal figure shows the resulting linear stresses of the shear -- tension in one diagonal and compression on the other. If you extend these diagonal lines around the surface of the tube, (and torsional shear is always greatest at the surface) then you get two interlaced spirals around the body of the tube.

One spiral is in compression and the other spiral is in tension. The two lines of stress are oriented 90 degrees from one another, and they are both 45 degrees off the longitudinal axis of the tube.

"Wait!" you say, "What about the double pendulum?" Well, since you askedů

Two linked pendula that swing with a 90 degree offset from one another make a dynamic curve, called a harmonic curve, also called a Lissajous figure. It can take on very many shapes, all mathematically similar, but one form of the harmonic curve looks like this :

Two components of opposed stress at 90 degrees form an interlaced spiral relationship, so do linked pendula operating at 90 degrees offset.

Double pendulum action occurs in, dare I say, all actions of the human body's balance and limbs. Torsional stress occurs in all actions of the human torso and limbs. This understanding shows that the lines of interlaced compressive and tensile stress (in-yo) link the two sides of the body without muscular contribution -- if the form of the body is collinear with the stresses.

To illustrate, place both arms in tegatatana, turn palms and elbows out, raise one arm and lower the other -- Voila! An upper spiral engaegd at the "upper cross" of the back. Now in this position, stand with feet at shoulder width, and turn on the heels and balls of your feet without stepping, twisting down until your kneecap touches the back of the other knee. You are a stable continous spiral form coincident with the torsional stress lines. This is tenchi posture - and what has been shown somewhat statically with very large form, can also be managed dynamically (with greater developed control) in much smaller progressive spiral forms or waves.

If one addresses a line of stress, say compressive stress, and pushes on it (compressing), well, you just pushed against what is already "sprung" to push back. If, on the other hand, you compress the tension line of stress, you relieve the stress on the structure, and it cannot resist without reversing its internal stress. Conversely, if you exert tension along the tension line -- it is already "sprung" to pull back. If you tense the compressive line however, you relieve its stress, which it is impossible to resist, unless the internal stress is reversed.

If I actuate the structure using this same mode, by prestressing the structure and connection along a compression line of stress, by relaxing the compressive stress -- the structure extends ("pushes") along the compression line, Conversely, if I prestress the structure in tension, and engage along the tencison stress line, and relax, the structure contracts ("pulls") along the tension stress line. In fact If I keep the intergity of the body whole, I do both at the same time on different sides.

This mode is distinct from using musculature to "push" or "pull" because the pre-stressing of the structure allows it to "relax" into the load along an appropriate line of stress, such that it cannot over-actuate, as muscles do if making active compensatory (resistant) strains.

If the structure is linked (jointed), and an applied extension or contraction is applied so as to relieve the target's internal stress along the torsional lines --the reduction of stress causes the limb (or torso) to tend to buckle (gyrate) outside the spiral torsional line of stress supporting it against the loads-- at which point it can exert neither tension nor compression in response, (and the sudden discontinuity typically reverses the applied stress profile, often catastrophically).

Reversing stress in a continuous mode without buckling, requires a smooth transition of form and energy at the same time. It is the form of a wave, spiral, like the stress lines, but cycling from positive to negative (like the top or bottom of the Lissajous curve noted above, or the top and bottom limits of the torsion tube structure, since all the stresses have to be resolved within the structural limits. If it does not resolve, then the structure must move to relieve the structural stress. Thus, at the major discontinuities -- the lower limit of the structure, (Earth) and the upper limit of thew struture ( heaven) compression on one side spiral resolves to tension on the opposite side spiral at the top of the structure, and tension on one side resolves to compression on the other side at the bottom.

At any discontinuity in the linked structure, the same reversal can occur (and already exists -- at a small amplitude). A small cycle of stress waves (kokyu in-yo ho) will "find" a discontinuity. A resonant cycle of stress waves will maximize the discontinuity signal (furitama). A counter-phase pulse of stress waves (or conversely the intersection of a counter-phase shape, which is equivalent) into the discontinuity will cause it to buckle and lose all structural integrity allowing displacement by the connection struture. (kokyu tanden ho)

Because the body's tendon stretch reflexes are conditioned to respond to sudden losses of structural integrity, they come into play. If a tendon is stretched suddenly there is a reflex action (e.g. -- the knee reflex), too fast for the conscious compensation to stop. A sudden wave of stress through the structure of sufficient amplitude AND at the resonance frequency (the structure itself amplifies the wave) induces a non-linear tendon stretch, triggering the stretch reflex associated with any tendon which is already in discontinuity.

Because the triggering phase is followed by the reversed phase of the stress wave, if the reflex is triggered, the reflex overactuates with respect to the oncoming counter-phase of the wave. The joint buckles out of the line of stress, and structural integrity is lost. The mechanism of structural integrity is exploited in a critical way to destroy that integrity. Shear is the name of that mechanism and in a body free to rotate, spiral action is the form of that eccentric shear.

This is one way to look at the integration of structure and dynamic in Aiki. The discussion on strikes and resonance in my blog looks at other issues, as does a discussion there on mass transfer and angular momentum chains. One point that I dealt with off-line with another poster here, helpfully pointed out an error in my interpretation of the mass transfer math, (adding an additional square term which was a already implicit in the interaction). The intuitive appeal of the error, I now realize, was my sense of the size off the disparity in input to reaction in actual engagements. That disparity, i now realize has much to do with the resonance and reflexive effects on the target , more so than the actual effective energy of the delivered input.

All of these points are suitable for adapting a structure to structural stress or dynamic loads as they are in disrupting it with structural stress or dynamic loads. The interplay can become quite complex between individuals with good training.